so the triangle has sides, 7, 8 and 9
find the angle opposite the 9 side first, calling it Ø
and using the cosine law.
9^2 = 7^2 + 8^2 - 2(7)(8)cosØ
81 = 49+64 -112cosØ
cosØ = 32/112
Ø = 73.398..° (I stored that in my calculator memory for future accuracy)
let x be the angle opposite the side 7
sinx/7 = sin73.398/9
sinx = .745356
x = 48.19°
so the third angle is 180-48.19-73.398 = 58.41°
three circles of radie 3,4, and 5 units respectively are tangent to each other eternaly. find the angle of the triangle formed by joining centers?
help plz
3 answers
thanks sir
you are welcome
little trick...
when finding the angles in a triangle given the 3 sides, you will of course have to use the cosine law to find one angle, then you can use the sine law to find a second angle.
Always find the largest angle first using the cosine law.
That way if the angle is obtuse, that problem is out of the way.
Using the sine law, gives you two possible answers, one acute and one obtuse.
Since a triangle can have at most only one obtuse angle, if you found it using the cosine law, the ambiguous case of the two answers is eliminated.
little trick...
when finding the angles in a triangle given the 3 sides, you will of course have to use the cosine law to find one angle, then you can use the sine law to find a second angle.
Always find the largest angle first using the cosine law.
That way if the angle is obtuse, that problem is out of the way.
Using the sine law, gives you two possible answers, one acute and one obtuse.
Since a triangle can have at most only one obtuse angle, if you found it using the cosine law, the ambiguous case of the two answers is eliminated.
0 answers